The dungeon aesthetic is tricky and elusive. At its core is the idea that the adventurers are treasure hunters and explorers venturing into an environment that is itself a deadly dangerous antagonist. If the adventurers become lost, they might die of thirst or starvation. If their light-source fails, they might stumble into natural hazards that would otherwise be easily avoided. Of course there are also fatal traps to be watchful for, as well as the creatures and monsters which inhabit the labyrinth.
Although the adventurers might sometimes be forced to fight for their lives, this is not an attrition-based skirmish-level combat game. Fights are somewhat rare and often better avoided - every opponent is potentially deadly and every combat is important. Combats are also over with quickly; in general the rules don't provide an arena for making tactical decisions; rather they're invoked from time to time as needed to generate or access important information.
Most of play is spent in free-form or "systemless" mode. The GM describes situations and provides sensory information (What do the adventurers see? What do they hear? What do the walls feel like? Are there any smells? Tastes?). The players are in charge of their characters, describing their actions. The GM provides cause and effect by inventing consequences. Generally, common sense prevails.
From time to time the GM will invoke the system by calling for an Ability check on one of a character's six abilities (STR, DEX, CON, INT, WIS, CHA) to discover if the character can do what the player wanted. Abilities are rated from 3 to 18. If the character has a related skill, the skill's rating is added to the Ability score as a bonus (in which case the procedure could more properly be called a Skill check.) The GM may apply a temporary bonus (+) or penalty (-) to the rating to represent important situational features. The player rolls 1d20. If the roll is equal to or less than the total ( Ability + [Skill] + [Bonus / Penalty] ) then the character is able to do whatever it was the player wanted.
Otherwise, the character can't do whatever it was the player wanted, and the GM invents the consequences. The door is too stuck, the boulder is too heavy, the chasm is too wide (and the character falls to his doom!) Ability checks show what characters can and can't do - not what they DO do. If the Ability check fails, the character can't succeed unless and until the situation changes favorably in some way.
Example: Boron the Really Strong (STR 17) wants to force a door. The door is jammed from the other side with iron spikes, so the GM assess a -2 penalty, making the final target 15. Boron rolls a 19! The door is too stuck even for Boron's mighty thews. There's nothing he can do for the time being. Boron must find another way to go, or return later with a battering ram (or a sorcerer who knows "Knock.")
How did the GM know how big to make the penalty? He just made it up! The dungeon is mysteriously dark and dangerous; not every door or every iron spike is the same. Consistency isn't the most important thing. In general, though, penalties and bonuses are small - no more than (+/-) 5, which represents a relatively vast 25% chance! If there are a host of interesting factors at work there's no need to enumerate them - the GM just assigns one number to represent all of them.
Ability (Skill) rolls are made to learn whether or not a character can do something the player wants. Sometimes, though, the GM will call for a Saving Throw. Each character has a saving throw (determined by class) that improves as the character gains levels. For some rolls the saving throw is modified by one of the character's Ability modifiers. Saving throws work just like Ability checks, except that they determine whether or not the character was able to avoid or resist some hazardous event.
# 19 -9 = 10 -3 = 7, 6, 5
Melee Attack: d20 + STR modifier + to-hit bonus (from level) + size modifier
Ranged Attack: d20 + DEX modifier + to-hit bonus (from level) + size modifier + range penalty
Defense: 10 + DEX modifier + defense bonus (from level) + size modifier + shield bonus
Damage: Melee Attack - Defense + Weapon - Armor
To be continued...